duplicating a surface and making it a child node
Duplicate, separate and parent

To get the surface you'll have to duplicate the faces.

  

Enable Edit Mode, select the faces you need, duplicate them by pressing shift+d.
Your new faces shall now be selected, but they still belong to the cube object.

To separate them press p while the faces are still selected. Choose "Separate" in the pop up menu to tell blender that you want to put those faces in a different object with "selection" criteria.

Now that you have two diffeent object you can parent with hierarchy.